Formal:
* Gratulor tibi! (I congratulate you!) This is a formal and direct way to express congratulations.
* Gratulationes tibi! (Congratulations to you!) This is a more traditional and slightly more poetic way to say it.
Informal:
* Feliciter! (Congratulations!) This is a short and informal way to express congratulations. It literally means "happily!"
* Bene factum! (Well done!) This is another informal way to say congratulations, especially when someone has achieved something difficult or challenging.
For a specific achievement:
* You can use a phrase like "Gratulor tibi de [achievement]" (I congratulate you on [achievement]) or "Feliciter propter [achievement]" (Congratulations on [achievement]).
The best way to choose the right phrase depends on the situation and your relationship with the person you are congratulating.